Mesenchymal stem cells (MSC) have been shown to have immunosuppressive properties. Following a bone marrow/peripheral blood stem cell transplant, a proportion of patients develop a condition called ‘graft versus host disease’ (GVHD). In this condition the transplanted cells recognize the recipient as foreign and bring about an immune-mediated destruction of tissues. The treatment for this condition is to use drugs that will cause immunosuppression. A small subset of these patients develop a severe form of GVHD (Grade III or IV) which, in spite of the best currently available treatment, is associated with eventual death in more than 90% of cases. The investigators propose to use infusions of expanded MSC from the donor to treat this condition. A few reports on this approach have already been published in peer reviewed journals and preliminary results appear to be promising. The investigators are also aware that larger trials have been initiated to study this. After getting written informed consent, the investigators will infuse expanded MSC into patients who develop steroid-resistant GVHD.